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In 1969, Graham developed a well-known response time bound for a DAG taskusing the total workload and the longest path of the DAG, which has been widelyapplied to solve many scheduling and analysis problems of DAG-based tasksystems. This paper presents a new response time bound for a DAG task using thetotal workload and the lengths of multiple long paths of the DAG, instead ofthe longest path in Graham's bound. Our new bound theoretically dominates andempirically outperforms Graham's bound. We further extend the proposed approachto multi-DAG task systems. Our schedulability test theoretically dominatesfederated scheduling and outperforms the state-of-the-art by a considerablemargin.

Bounding the Response Time of DAG Tasks Using Long Paths